On the earhole again

The New Partridge Dictionary of Slang and Unconventional English is your friend.

On the ear 'ole On the scrounge UK Extends the sense of ear 'ole ( whatever you can hear) to 'whatever you can pick up'.

Jonathon Green, Chambers Slang Dictionary (2008) has this entry for "on the earhole":

on the earhole (also on the happy New 'Ear) {one is talking into a victim's earhole} {1910s+} (UK Und.) on the scrounge.

Evidently, scrounge as used here refers to something inhabiting the borderlands between cadging, scavenging, and stealing.

Eric Partridge, A Dictionary of Slang and Unconventional English, second edition (1938) reports that the phrase is of military origin:

ear-hole, on the. Cadging (esp. money): military : C. 20. F[raser] & Gibbons [Soldier and Sailor Words and Phrases, 1925].

As Partridge suggests, Fraser & Gibbons, Soldier and Sailor Words and Phrases (1925) does have a brief entry for the term:

EARHOLE, ON THE : Cadging. Trying to borrow.

Tony Thorne, The Dictionary of Contemporary Slang (1990) has this for the term:

on the earhole/ear'ole adj, adv British cadging, trying to borrow money. An old London working class expression still heard in the 1980s. For the etymology, see ear'ole. [Under ear'ole as a noun referring to "a dull, gormless or exasperating person," Thorne offers this note on the term's origin: "The eighth edition of Eric Partridge's Dictionary of Slang and Unconventional English quotes a 1976 article in New Society which derives ear'ole from those (pupils) who listen and obey, as opposed to those who act or refuse to conform. This is likely to be a folk etymology (and probably spurious) as the word was in use as long ago as the 1950s as a non-specific term of abuse."]

So Green thinks that the person "on the earhole" is talking into the victim's ear; Partridge (citing Fraser & Gibbons) suggests that it may have begun as a reference to wheedling money out of someone; and Thorne seems to have a similar origin in mind. In any case, the expression goes back at least to the mid-1920s and very likely to the Great War.

Noel Smith, The Criminal Alphabet: An A-Z of Prison Slang (2015) offers a very different theory:

ON THE EARHOLE To be on the earhole is to be looking out for something for nothing. Somebody who is always on the cadge or looking to borrow things is on the earhole. It comes from a time when there was a strict rule of silence in UK prisons, and prisoners weren't allowed to speak to each other. They developed a sign language in order to communicate and touching your ear meant that you wanted to borrow something, so to this day someone who is on the ponce is said to be on the earhole.

But if all you accomplish by touching your ear is to indicate that you want to borrow something— not giving even a hint about what you want to borrow—it doesn't make an especially useful signal. Also, if this term originated as prison slang, it seems odd that researchers who traced it back to World War I never noticed or mentioned that fact. I am quite skeptical of Smith's explanation here, although I have no doubt that it means what he says it means today in prison slang.

'...But if all you accomplish by touching your ear is to indicate that you want to borrow something — not giving even a hint about what you want to borrow — it doesn't make an especially useful signal...'

My father was a prison officer in the UK in the 1950's.

It was more likely to have been used to warn another prisoner that someone else was on the scrounge, so beware. In which case it was a really useful signal and far from complementary, so unlikely to have been used in respect to one’s self.